The generator buffer is just a buffer amplifier with a 50R input impedance and a low output impedance.
Yes and yes to your last two questions.
50 ohm impedance is required to properly terminate signals to prevent reflections and all of the other nasties. Those only come into play with higher frequencies, so I imagine that whoever designed your training course, decided on the buffer amplifier to simplify things, so your function generator becomes an approximation of an ideal one, instead of having to keep thinking of the output impedance.